# 2014 April(71H) Math Question 1

Choice A

it says that "Danica will donate $35.00, plus$0.07 for each book donated by her classmates.", and that her classmates donated b books:

d = 35 + 0.07b

# 2014 April(71H) Math Question 2

Choice K

z = -16 × (-4) = 64

# 2014 April(71H) Math Question 3

Choice D

Rule name Rule Example
Product rules a na m = a n+m 23 ⋅ 24 = 23+4 = 128
a nb n = (a b) n 32 ⋅ 42 = (3⋅4)2 = 144
Quotient rules a n / a m = a nm 25 / 23 = 25-3 = 4
a n / b n = (a / b) n 43 / 23 = (4/2)3 = 8
Power rules (bn)m = bn⋅m (23)2 = 23⋅2 = 64
bnm = b(nm) 232 = 2(32)= 512
m√(bn) = b n/m 2√(26) = 26/2 = 8
b1/n = nb 81/3 = 38 = 2
Negative exponents b-n = 1 / bn 2-3 = 1/23 = 0.125
Zero rules b0 = 1 50 = 1
0n = 0 , for n>0 05 = 0
One rules b1 = b 51 = 5
1n = 1 15 = 1
Minus one rule (-1)n = -1 , n odd v
(-1)n = 1 , n even
(-1)5 = -1
Derivative rule (xn) = nx n-1 (x3) = 3⋅x3-1
Integral rule xndx = xn+1/(n+1)+C x2dx = x2+1/(2+1)+C

4b8⋅5b3 = 4⋅5⋅b8+3=20b11

# 2014 April(71H) Math Question 4

Choice K

The Exterior Angle Theorem states that, for a triangle:

• The exterior angle d equals the angles a plus b
• The exterior angle d is greater than angle a, or angle b.

Therefore, ∠PRS = 40° + 105° = 145°

# 2014 April(71H) Math Question 5

Choice D

Let the larger number be L, the smaller number be S:

L + S = 90

L = S + 50

⇒ S = 20, L = 70

# 2014 April(71H) Math Question 6

Choice G

The absolute value of a number is its distance from zero on a number line.

|7 - 5| - |1 - 8| = 2 - 7 = -5

# 2014 April(71H) Math Question 7

Choice E

$$3^{2}+2+(-3)^{2}-3=17$$

# 2014 April(71H) Math Question 8

Choice G

$$(x^{2}+2x)+(3x+5)+(x^{2}+1)+(6x-4)$$ $$=(x^{2}+x^{2})+(2x+3x+6x)+(5+1-4)$$ $$=2x^{2}+11x+2$$

# 2014 April(71H) Math Question 9

Choice E

Let the number of Tough Cuts be T, the number of Easy Pushes be E,

T + E = 96

T = 2E

⇒ E = 32, T = 64

# 2014 April(71H) Math Question 10

Choice H

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

In descending order, the set of numbers is:

116, 142, 175, 186, 191, 201, 201

Median = 186

# 2014 April(71H) Math Question 11

Choice C

(50 – 20) inches / 5 years = 6 inches

# 2014 April(71H) Math Question 12

Choice G

The area of a triangle is given by the equation:

Area= (1/2) × base × height

Therefore,

Area= (1/2) × 16 × 12 = 96

- Cost

Choice C

# 2014 April(71H) Math Question 17

Choice A

For any fraction, the greater its numerator and the lessor its denominator, the greater the value of the fraction.

Among the choices, d / a has the greatest numerator d and the least denominator a.

# 2014 April(71H) Math Question 18

Choice J

Let the number of extra hours Maurice worked beyond 40 hours be E:

# 2014 April(71H) Math Question 43

Choice C

Let’s divide all the possible …

# 2014 April(71H) Math Question 44

Choice F

Let the number of Style …

Choice D

200 × 1.6 = 320

Choice J

3x + 5y = 17 …

# 2014 April(71H) Math Question 47

Choice E

The least common multiple is …

# 2014 April(71H) Math Question 48

Choice G

The slopes of two lines …

# 2014 April(71H) Math Question 49

Choice A

Graphing an inequality on a …

# 2014 April(71H) Math Question 50

Choice G

Total surface area = ½ …

Choice C

1 # 2 = 1 …

# 2014 April(71H) Math Question 52

Choice G

When a point is translated …

# 2014 April(71H) Math Question 53

Choice C

What you need to know …

# 2014 April(71H) Math Question 54

Choice K

What is looks like is …

# 2014 April(71H) Math Question 55

Choice D

When parallel lines get crossed …

# 2014 April(71H) Math Question 56

Choice G

ME = AM – AE = AM – BN = 5 – 1 = 4;

MN = 8

⇒ AB = CD = EN = √(ME² + MN²) = 4√3

arc AMD = 2/3 ⋅ 2π ⋅ 5 = 20/3 ⋅ π

arc BNC = 1/3 ⋅ 2π ⋅ 1 = 2/3 ⋅ π

⇒ Length of the belt = arc AMD + AB + arc BNC + CD = 20/3 ⋅ π + 4√3 + 2/3 ⋅ π + 4√3 = 22/3 ⋅ π + 8√3

# 2014 April(71H) Math Question 57

Choice E

It should be remembered that:

sin2 A + cos2 A = 1

⇒ cos A = ± 12/13

As can be seen from the diagram, in the domain from 0 to 2π (0°-360°), it is possible for cos A to be negative.

# 2014 April(71H) Math Question 58

Choice F

We should recognize that the …

# 2014 April(71H) Math Question 59

Choice D

An arithmetic sequence is a …

# 2014 April(71H) Math Question 60

Choice K

The graph crosses the x-axis …